Persistence of travelling wave solutions of a fourth order diffusion system

Authors:
Y. N. Kyrychko;M. V. Bartuccelli;K. B. Blyuss
Affiliations:
Department of Mathematics and Statistics, University of Surrey, Surrey Lane, Guildford, Surrey GU2 7XH, UK;Department of Mathematics and Statistics, University of Surrey, Surrey Lane, Guildford, Surrey GU2 7XH, UK;Department of Mathematical Sciences, University of Exeter, Exeter, Devon EX4 4QE, UK
Venue:
Journal of Computational and Applied Mathematics
Year:
2005

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Abstract

In this paper the extended Burgers-Huxley equation with the fourth-order derivative is considered. First, the convergence to the uniform steady state is proved, which means the solution of the equation with positive initial data will remain positive for time t sufficiently large. Then, the persistence of the travelling wave solution for the extended equation on the unbounded domain is investigated. We have proved that this solution will persist under small perturbation of the equation.